Calculations for the practical applications of quadratic helicity in MHD

Akhmet’ev, P. M., Candelaresi, S. and Smirnov, A. Y. (2017) Calculations for the practical applications of quadratic helicity in MHD. Physics of Plasmas, 24(10), 102128. (doi: 10.1063/1.4996288)

Abstract

For the quadratic helicity χ(2), we present a generalization of the Arnol'd inequality which relates the magnetic energy to the quadratic helicity, which poses a lower bound. We then introduce the quadratic helicity density using the classical magnetic helicity density and its derivatives along magnetic field lines. For practical purposes, we also compute the flow of the quadratic helicity and show that for an α2-dynamo setting, it coincides with the flow of the square of the classical helicity. We then show how the quadratic helicity can be extended to obtain an invariant even under compressible deformations. Finally, we conclude with the numerical computation of χ(2) which show cases the practical usage of this higher order topological invariant.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Candelaresi, Dr Simon
• Authors: Akhmet’ev, P. M., Candelaresi, S., and Smirnov, A. Y.
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Physics of Plasmas
• Publisher: AIP Publishing
• ISSN: 1070-664X
• ISSN (Online): 1089-7674
• Published Online: 24 October 2017
• Copyright Holders: Copyright © 2017 AIP Publishing
• First Published: First published in Physics of Plasmas 24(10): 102128
• Publisher Policy: Reproduced in accordance with the publisher copyright policy